For diagonal D and aspect ratio a:b, width = D × a ÷ √(a² + b²) and height = D × b ÷ √(a² + b²). The answer uses the same unit as D. For 16:9, width ≈ 0.871576D and height ≈ 0.490261D, so a 27-inch screen is about 23.53 × 13.24 inches.
Use aspect ratio, not pixel count
A diagonal alone cannot determine both dimensions; the aspect ratio supplies the shape. If you know the resolution, reduce pixel width and height by their greatest common divisor: 1920×1080, 2560×1440 and 3840×2160 all reduce to 16:9 and therefore have the same physical width and height at the same diagonal. The full pixel counts matter for PPI, but not for physical dimensions once the ratio is known.
Common 16:9 widescreen dimensions
Visible width × height, rounded to two decimals: 24 in → 20.92 × 11.77 in; 27 in → 23.53 × 13.24 in; 32 in → 27.89 × 15.69 in; 43 in → 37.48 × 21.08 in; 55 in → 47.94 × 26.96 in; 65 in → 56.65 × 31.87 in. Enter a diagonal in centimeters to get centimeters, or multiply inches by exactly 2.54.
Use the visible active area
Bezels and housing are outside the panel rectangle. If you measure hardware, measure the active image diagonal rather than the outside case, and expect small differences from rounded advertised sizes.